This quantity is a lower bound for \(I(X,Y)\) , and such a network is called a statistics network in the Mutual Information Neural Estimator (MINE) framework developed by [1]}. Given the universal approximation theorem for neural networks [2]}, [3]}, one may expect to get through \(\tilde{I}_\psi (X,Y)\)  an arbitrarily tight bound given that the network complexity is high enough. Details about the network architecture for \(T_\psi \)  used in the paper are given in the appendices.
